Measure out the peanut butter first so it's ready to go.
In a mixing bowl, cream the softened butter, white sugar, and packed brown sugar together for about 2 minutes, until light and fluffy.
Add the egg, vanilla, and peanut butter. Mix until well combined, scraping down the bowl a time or two.
Stir together the flour, salt, and baking soda. Add to the dough about a third at a time, mixing between additions, until just combined.
Fold the Rice Krispies cereal in by hand with a spatula. Don't use the mixer for this step — it will crush the cereal.
Scoop the dough onto a baking sheet, leaving room for the cookies to spread (about 8 per pan). Chill the scooped dough in the refrigerator for about 1 hour.
Bake at 350°F for 9 to 11 minutes, until the cookies have flattened out, the tops look crackly, and the edges are just starting to brown.
Let cool on the pan for a few minutes before serving.